where \(t\)  represents continuous time, \(x\)  is the state variable, \(F\)  is a function determining the flow of this system, and \(\tau >0\)  is the delay period. This system is capable of exhibiting rich nonlinear behavior including periodic oscillations and deterministic chaos depending on the system parameter setting. In the first proposal of a single-node reservoir with delayed feedback [1]}, the reservoir was implemented using electronic circuits with a feedback loop (see Sec. REF  for details). As shown in Fig. REF , the input signal is time-multiplexed by a mask function [2]} and fed to the single nonlinear node. The virtual nodes are set at \(N\)  time points that equally divide the delay period \(\tau \) . The time interval between two consecutive nodes is \(\theta \equiv \tau /N\) . The states at these virtual nodes, \(x(t-(N-i)\theta )\)  for \(i=1,\ldots ,N\) , are used as the reservoir state at time \(t\)  and then fed to the output layer through weighted connections. These connection weights are trained in the readout. The system was successfully applied to the spoken digit recognition task and the nonlinear autoregressive moving average (NARMA)-10 time series prediction task.
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